2. Suppose that A(t) is the matrix:t2 t3t t2tA(t) :1tand that o1, Ø2, P3 are solutions to the ODEy' + A(t)y = 0, t> 0that satisfy:(3)2.а$1(1) :, Ø2(1) =$3(1) =-2for some constants a, b, c E R. Calculate the Wronskian W[¢1, ¢2, Ø3] and show that {¢1,$2, $3}is a fundamental set of solutions.

given matrix At=tt2t31tt2t-11t according to question ϕ1 , ϕ2 , ϕ3 are solution of the ODE y'+Aty=0…

t2 t3 -() A(t) 1 t t2 1 t and that 1, 02, 03 are solutions to the ODE y' + A(t)y = 0, t>0 that satisfy: a $1(1) = , $2(1) = 3,03(1) = C -2 for some constants a, b, c E R. Calculate the Wronskian W[o1, $2, $3] and show that {01, ¢2, $3] is a fundamental set of solutions.

t2 t3 -() A(t) 1 t t2 1 t and that 1, 02, 03 are solutions to the ODE y' + A(t)y = 0, t>0 that satisfy: a $1(1) = , $2(1) = 3,03(1) = C -2 for some constants a, b, c E R. Calculate the Wronskian W[o1, $2, $3] and show that {01, ¢2, $3] is a fundamental set of solutions.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

2. Suppose that A(t) is the matrix:
t2 t3
t t2
t
A(t) :
1
t
and that o1, Ø2, P3 are solutions to the ODE
y' + A(t)y = 0, t> 0
that satisfy:
(3)
2.
а
$1(1) :
, Ø2(1) =
$3(1) =
-2
for some constants a, b, c E R. Calculate the Wronskian W[¢1, ¢2, Ø3] and show that {¢1,$2, $3}
is a fundamental set of solutions.

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